Tangent = opposite side / adjacent
Tangent M = m/p
Let
x--------> the speed of the girl in step
y--------> the speed of the escalator in step
d------> the distance between ground and floor.
we know that

when the girl is going up on escalator
----> equation 
when the girl is going down on escalator
-------> equation 
Adds equation
and equation 

--------> equation 
Time to climb (in step) with y=0 (escalator standing still)
-----> equation 
Substitute equation
in equation 

therefore
the answer is

Step-by-step explanation:
Hey there!
Here;
The equations are;


Multiplying equation (i) by 2.
16x + 14y = 78
<u>4</u><u>x</u><u> </u><u>-</u><u> </u><u>1</u><u>4</u><u>y</u><u> </u><u> </u><u> </u><u>=</u><u> </u><u>-68</u>
20x = 10

x = 1/2.
Putting value of 'x' in equation (i).




Therefore the value of y is 5.
<u>Check</u><u>:</u>
<u>Put</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>x</u><u> </u><u>and</u><u> </u><u>y</u><u> </u><u>in</u><u> </u><u>equation</u><u> </u><u>(</u><u>i</u><u>)</u><u>.</u>
8x + 7y = 39



(True).
<u>Therefore</u><u>, </u><u>the</u><u> </u><u>solution</u><u> </u><u>is</u><u> </u><u>;</u><u> </u><u>(</u><u>1</u><u>/</u><u>2</u><u>,</u><u>5</u><u>)</u><u>.</u>
<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>